Vestnik KRAUNTS. Fiziko-matematicheskie nauki

7-11

Authors: L. Kh. Gadzova

The asymptotics of the fundamental solution of the linear ordinary differential equation of fractional order with constant coefficients, for large values of spectral parameter λ is found.

18-23

Authors: A. Kh. Kodzokov, Z. O. Beslaneev, A. L. Nagorov, M. B. Tkhamokov

The paper discusses ways to solve linear Diophantine equations in the particular case of two unknowns, and, in general, with a few unknowns. The main result is contained in Theorem 1, which provides a general method for solving any Diophantine equation, based on a comparison of the relevant module.

28-33

Authors: Z. S. Madrakhimova

This paper deals with the formulation and study of boundary value Gellerstedt type problem for parabolic-hyperbolic equation with degeneration of the type and order within the area which equivalently reduced to integral equations.

43-49

Authors: I.V. Drobysheva

The paper presents a mathematical model hereditarity Duffing oscillator with friction, which is a generalization of previously known classical model of Duffing oscillator. This generalization is replaced in the model equation integral derivative on derivatives of fractional order in the sense of Riemann-Liouville. Built explicit finite difference scheme for calculating approximate solutions, as well as the phase trajectories for different values of the control parameters.

55-61

Authors: D.V. Makarov

The paper presents a mathematical model that generalizes the famous Kondratiev cycles model (model Dubovskiy) used to predict economic crises. This generalization is to integrate the memory effect, which occurs frequently in the economic system. With the help of numerical methods, to receive a generalized model, according to which the phase paths have been built.

68-72

Authors: M. B. Tkhamokov, A. L. Nagorov, Z. O. Beslaneev, A. Kh. Kodzokov

This article attempts to estimate the entropy Karachay-Balkar printed texts. As of the object were taken by famous national writers, as well as the texts of periodicals. With this program, written by the authors calculated the frequency of the letters, different combinations and phrases modeled on the basis of the results obtained. When calculating performance used known standard techniques. An entropy to the twenty-fifth day of the order and the value of the redundancy of the language. The results of studies of domestic and foreign authors in the field of counting entropy. A comparative analysis of the different orders of the entropy for European languages.

79-89

Authors: O. K. Zhdanova

This article presents the materials of the seminar held for mathematics teachers and all those interested in similar problems in Vitus Bering Kamchatka State University. The seminar was devoted to solving problems with parameters and the high level problems of the Unified State Exam.